It is desirable to provide relatively simple means for measuring a position along a line, either straight or curved, or on a planar or other curvilinear surface, with a high degree of accuracy at a reasonable cost. One example of the use of such a measuring device is exemplified by presently known navigation apparatus which use attitude readout devices for determining the angular orientation of an object relative to a set of reference axes for use in inertial navigation systems, for example. In addition, it is often desirable to know the position of an object with respect to a reference point along a line or on planar or curved surfaces. Further, it may be desirable to determine the angular position of a rotating object with respect to a reference angle.